Related papers: On Arnold's and Pushkin's puzzles
Some particular facets of the numerous works by Marcos Moshinsky and Yurii Fedorovich Smirnov are presented in these notes. The accent is put on some of the common interests of Yurii and Marcos in physics, theoretical chemistry, and…
We approach several themes of classical geometry of the circle and complete them with some original results, showing that not everything in traditional math is revealed, and that it still has an open character. The topics were chosen…
Three versions of Luca Pacioli's 'De Dvina Proportione' remain: a manuscript held in Milan, another in Geneva and a printed version edited in Venice. A recent book, 'Antologia della Divina Proporzione', has all three in one volume, allowing…
We prove a recent conjecture by Ulas on reducible polynomial substitutions.
Lectures notes (in italian) of some arguments of classical analysis, with exercises. A particular emphasis to functional analysis and elementary operator algebra theory is given, by means of exercises and examples.
We solve a problem concerning Euler's paper "Variae considerationes circa series hypergeometricas" (\cite{E661}) suggested by G. Faber in the preface to Volume 16,2 of the first series of Euler's Opera Omnia by methods proven by Euler on…
Vladimir Shpilrain and Jie-Tai Yu have asked for an effective algorithm to decide if two elements of C[x,y] are related by an automorphism of C[x,y]. We describe here an efficient algorithm that decides this question and finds the…
We prove the conjectures on dimensions and characters of some quadratic algebras stated by B$.$L$.$Feigin. It turns out that these algebras are naturally isomorphic to the duals of the components of the bihamiltonian operad.
In introductions to the subject for a general audience of mathematicians or logicians, the univalence axiom is typically explained by handwaving. This gives rise to several misconceptions, which cannot be properly addressed in the absence…
Evolomino is a pencil-and-paper logic puzzle popularized by the Japanese publisher Nikoli (like Sudoku, Kakuro, Slitherlink, Masyu, and Fillomino). The puzzle's name reflects its core mechanic: the shapes of polyomino-like blocks that…
Boris Shoikhet noticed that the proof of lemma 1 in section 2.3 of math.QA/0504420 contains an error. In this note I give a correct proof of this lemma which was suggested to me by Dmitry Tamarkin. The correction does not change the results…
Classes of linguistic paradoxes and linguistic tautologies are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic. The general cases exposed below are…
We answer a question raised in ``Peripheral elements in reduced Alexander modules'' [J. Knot Theory Ramifications 31 (2022), 2250058]. We also correct a minor error in that paper.
Andrews once gave $q$-analogues of a binomial congruence of Glaisher, and he suggested perfect $q$-analogues. In this note we give ones meeting the demand of Andrews.
In this paper, we first prove the existence of solutions to Dirichlet problems involving the fractional $g$-Laplacian operator and lower order terms by appealing to sub- and supersolution methods. Moreover, we also state the existence of…
The present work is a user's guide to the results of a previous paper by the second and third authors, where a description of the space of characters of a quasi-projective variety was given in terms of global quotient orbifold pencils.…
Sergey Pinchuk discovered a class of pairs of real polynomials in two variables that have a nowhere vanishing Jacobian determinant and define maps of the real plane to itself that are not one-to-one. This paper describes the asymptotic…
There is a big difference between "quasi-galois" in the eprint (arXiv:0907.0842) and "pseudo-galois" in the sense of Suslin-Voevodsky.
Projections onto several special subsets in the Dedekind complete vector lattice of orthogonally additive, order bounded (called abstract Uryson) operators between two vector lattices $E$ and $F$ are considered and some new formulas are…
In previous papers we define certain Lagrangian shadows of ample divisors in algebraic varieties. In the present brief note an existence condition is discussed for these Lagrangian shadows.